Simplified chemical reaction kinetic model construction method based on evolutionary algorithm

Abstract

The invention discloses a simplified chemical reaction kinetic model construction method based on an evolutionary algorithm, and relates to the field of computational fluid mechanics. Comprising the following steps: acquiring flame and detonation target characteristics such as laminar combustion speed, laminar flame thickness, adiabatic flame temperature, constant volume flame temperature, CJ detonation speed and half-reaction width according to experimental data or detailed chemical reaction mechanism; establishing a control equation set for describing a one-dimensional laminar flame and detonation development process, and taking a solving error of the control equation set as a target optimization function of an evolutionary algorithm; and solving the control equation set and iteratively optimizing simplified chemical reaction kinetic parameters such as activation energy, specific heat capacity ratio, combustion heat value, pre-exponential factor, thermal diffusion coefficient, relative molecular mass and the like in the equation set by adopting an evolutionary algorithm until the solving result can reproduce flame and detonation target characteristics. According to the method, chemical reaction kinetic parameters can be rapidly and reliably developed and simplified, flame and detonation characteristics can be reproduced in computational fluid dynamic analysis, and the calculation time is shortened.

Description

Technical Field

[0001] The present invention belongs to the field of computational fluid dynamics (CFD), and in particular relates to a method for constructing a simplified chemical reaction kinetics model based on an evolutionary algorithm. Background Art

[0002] With the rapid development of industry and the growth of economic construction needs, clean gas energy will usher in rapid development. Combustible gases such as hydrogen and natural gas (methane) have the advantages of large reserves and high conversion efficiency. Under the wave of energy transformation, this type of clean gas energy will play an important "bridge" role. However, if improperly operated or used, it may cause accidental fire and explosion risks. Especially in confined areas (such as pipelines or tunnels), when combustible gases accumulate and mix with air to ignite, the temperature and pressure rise rapidly, which may lead to detonation and cause serious consequences, such as damage to surrounding facilities and buildings and casualties. Combustible gas or flammable liquid vapor cloud explosion accidents occur frequently, so it is very important to carry out relevant research to improve safety in practical applications.

[0003] In recent years, with the development of high-performance computing technology and computational fluid dynamics technology, the study of the combustion and explosion laws of combustible gases through numerical simulation has become an important research method. The combination of numerical calculation, experiment and theoretical analysis is a good way to solve flow combustion problems. Many scientific decisions on gas industry pipeline design and fire protection plans have taken the results of combustion numerical simulation calculations as an important reference. In the process of computational fluid dynamics solution, in order to describe the deflagration, detonation and deflagration-to-detonation processes of combustible gases or combustible liquid vapor clouds, a suitable chemical reaction model is required. Currently, the commonly used chemical reaction models can be roughly divided into two categories: single-step chemical reaction models and detailed chemical reaction mechanism models. Among them, the single-step chemical reaction model is the most basic and most commonly used chemical reaction model, and its computational efficiency is high. However, compared with experimental data, the effectiveness of the simulation results and the accuracy of the data still have major problems. The detailed chemical reaction mechanism model has high computational accuracy and can describe the distribution of chemical reaction intermediates, but its control equation group has obvious rigidity problems in the computational fluid dynamics solution process. In order to ensure the stability of the calculation process and the accuracy of the calculation results, it is often necessary to use a very small solution time step, which will result in the solution process consuming a lot of time and computing resources. In addition, the development of the above two chemical reaction kinetics models also has a series of problems such as long development cycle, cumbersome process, narrow scope of application, and difficulty in taking into account both deflagration and detonation. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides a simplified chemical reaction kinetic model construction method based on evolutionary algorithm, which uses evolutionary algorithm and simplex method and other technologies to determine the optimal reaction kinetic parameters (activation energy, specific heat ratio, heat of combustion, pre-exponential factor, thermal diffusion coefficient, relative molecular mass) of the simplified reaction model that can reproduce the target characteristics of flame and detonation according to experimental data or target characteristics of flame and detonation (laminar combustion velocity, laminar flame thickness, adiabatic flame temperature, constant volume flame temperature, CJ detonation velocity, half reaction width). This method has the characteristics of high model accuracy, high development efficiency, wide application range, etc., and can be used for computational fluid dynamics simulation and theoretical analysis of phenomena such as deflagration, detonation, and deflagration to detonation, and can also be used for simulation calculation of diffusion flame.

[0005] In order to achieve the above technical objectives, the present invention adopts the following technical solutions:

[0006] A method for constructing a simplified chemical reaction kinetics model based on an evolutionary algorithm comprises the following steps:

[0007] Step 1, obtaining the combustible flame and detonation target characteristic parameters according to experimental data or by calculation of a detailed chemical reaction mechanism, wherein the combustible flame and detonation target characteristic parameters include laminar combustion velocity, laminar flame thickness, adiabatic flame temperature, constant volume flame temperature, CJ detonation velocity, and half reaction width;

[0008] Step 2, establishing a control equation group for describing the one-dimensional laminar flame and detonation development process, solving the control equation group to obtain flame and detonation characteristic parameters, wherein the flame and detonation characteristic parameters include laminar combustion velocity, laminar flame thickness, adiabatic flame temperature, constant volume flame temperature, CJ detonation velocity, and half reaction width;

[0009] Step 3, estimating the upper and lower limits of the value range of simplified chemical reaction kinetic parameters and the initial value of iteration, wherein the simplified chemical reaction kinetic parameters include activation energy, specific heat ratio, calorific value of combustion, pre-exponential factor, thermal diffusion coefficient, and relative molecular mass;

[0010] Step 4: Substitute the estimated iterative initial value in step 3 into the evolutionary algorithm to solve and obtain a set of optimized simplified chemical reaction kinetic parameters within the value range; substitute the optimized simplified chemical reaction kinetic parameters into the control equation group constructed in step 2 and solve the flame and detonation characteristic parameters;

[0011] Step 5, evaluating the solution error between the flame and detonation characteristic parameters obtained by solving the control equations in step 4 and the target characteristic parameters obtained in step 1, and using the solution error as the target optimization function of the evolutionary algorithm; if the error is greater than the threshold, continuing to use the evolutionary algorithm to iteratively optimize the simplified chemical reaction kinetic parameters and perform error evaluation until the solution error of the control equations meets the predetermined requirements;

[0012] Step 6: Use the simplex method to locally optimize the simplified chemical reaction kinetic parameters obtained in step 5 until the error of solving the control equation group is less than the set value; use the optimized simplified chemical reaction kinetic parameters in the computational fluid dynamics analysis to calculate and accurately reproduce the target characteristic parameters of the combustible flame and detonation.

[0013] Furthermore, step 1 includes: obtaining the characteristic parameters of the combustible flame and detonation target by conducting experimental measurements or using a detailed chemical reaction mechanism to solve the type of combustible; wherein, the laminar flame speed refers to the propagation speed of the flame surface relative to the unburned gas; the laminar flame thickness refers to the sum of the widths of the preheating zone and the chemical reaction zone; the adiabatic flame temperature refers to the temperature that the combustion products can reach when the combustible gas is completely burned under adiabatic conditions; the constant volume flame temperature refers to the temperature that the combustion products can reach when the combustible gas is completely burned under constant volume conditions; the CJ detonation velocity refers to the minimum detonation wave velocity calculated by simplifying the detonation wave into a one-dimensional discontinuous surface with infinite reaction rate in the Chapman-Jouguet theory; the half-reaction width refers to the distance between the position where the fuel mass fraction Y = 0.5 and the position where the shock wave surface is located in the detonation wave structure.

[0014] Furthermore, the step 2 comprises:

[0015] The control equations describing the heat conduction and energy release process are established to solve the one-dimensional laminar flame characteristic parameters:

[0016] (1)

[0017] (2)

[0018] (3)

[0019] (4)

[0020] (5)

[0021] in, Indicates the horizontal direction, represents the calculation of the initial density, represents the current density, T0 represents the initial temperature of calculation, T represents the current temperature, represents the specific heat at constant volume, represents the specific heat capacity at constant pressure, is the thermal diffusion coefficient, represents the chemical reaction source term, A represents the pre-exponential factor, represents the activation energy, Y represents the mass fraction of the unburned reactants, q represents the calorific value of combustion, represents the laminar flame speed, is the adiabatic flame temperature, represents the constant volume flame temperature, represents the laminar flame thickness, represents the maximum value of the absolute value of the temperature gradient, exp represents the exponential function, and R represents the universal gas constant;

[0022] Establish the governing equations for describing the detonation wave structure:

[0023] (6)

[0024] (7)

[0025] (8)

[0026] (9)

[0027] Where t represents time, U represents the flow velocity of the combustibles, represents the speed of sound under initial conditions, E represents the specific total energy, c represents the current speed of sound, represents the initial pressure, p represents the current pressure, represents the specific heat ratio, represents the CJ detonation velocity, represents the half-reaction width, and They represent the x-coordinates corresponding to the mass fractions of unburned reactants of 1 and 0.5 respectively. The flame and detonation characteristic parameters are obtained by solving the two sets of equations.

[0028] Furthermore, the step 3 comprises:

[0029] Each parameter uses a different value range, and the initial value of the iteration is the average of the upper and lower limits of the corresponding value range.

[0030] Furthermore, in step 4, a centroid-based evolutionary algorithm is adopted, and the centroid definition is used to create the evolution direction of individuals in the population. According to the target optimization function value, individuals with larger calculation errors in the population are moved to areas with smaller calculation errors in the value interval, thereby accelerating the convergence of calculation errors.

[0031] Furthermore, the evolutionary algorithm includes: determining the maximum evolutionary step length of the centroid-based evolutionary algorithm , the number of subpopulation individuals K, the data dimension D, determine the population size N = 2K × D; initialize the population containing N individuals according to the iterative initial value Population , , the data dimension of each individual is D, and an empty set V is established to store the newly generated individuals; when the calculated target optimization function value does not reach the stopping condition, K individuals are selected from the population P to form a sub-population , using subpopulation U s All individuals in calculate the current center of mass c according to formula (11) m ; In the interval Internal random value determines the evolution step length According to formula (10), from subpopulation U s Randomly select individuals And using the centroid c m Generate new individuals ; If the calculated objective optimization function value > , then the individual Join set V; take The first N individuals with the largest target optimization function value in the population P are used to update the population P; the above iterative optimization process is repeated until the target optimization function value calculated by the individuals in the population P reaches the predetermined stop criterion, and the best individual in the population P is output as the target optimization result; the best individual is the individual when the target optimization function value is the largest;

[0032] (10)

[0033] (11)

[0034] in, represents the new individuals generated in the population, represents an individual in the population P, represents the step length, c m Represents the use of subpopulation U s Calculate the centroid, Represents the subpopulation U s The individuals selected from represents the subpopulation U s Any individual in the population, W represents the total mass of individuals in the population, and f represents an arbitrary function relationship; These are the simplified chemical reaction kinetic parameters to be optimized. The data dimension D=6, which represent activation energy, specific heat ratio, calorific value of combustion, pre-exponential factor, thermal diffusion coefficient, and relative molecular mass respectively. The function relationship f is the error relationship between the solution of the control equations for laminar flame and detonation development process and the target value.

[0035] Furthermore, the error solution in step 5 includes:

[0036] The flame and detonation characteristic parameters ( , , , , , ) is compared with the target characteristic parameters in step 1 and the solution error is quantified. The solution error is defined as:

[0037] ;

[0038] Among them, error represents the solution error, i represents the flame and detonation characteristic parameter index, Represent the flame and detonation characteristic parameters respectively ( , , , , , ), Represents the corresponding target characteristic parameter. The evolutionary algorithm will minimize the solution error by optimizing and simplifying the chemical reaction kinetic parameters, that is, the solution error of the control equation group is used as the target optimization function of the evolutionary algorithm.

[0039] Further, the simplex method used in step 6 includes:

[0040] For n-dimensional optimization problems, we first construct an n+1-dimensional simplex, calculate the function values ​​of the simplex vertices, and then analyze and compare the vertex function values. We construct new vertices and simplexes through reflection, diffusion, contraction and other operations until the convergence conditions are met.

[0041] Beneficial effects:

[0042] The present invention can overcome a series of problems in the prior art such as long cycle, cumbersome process, narrow scope of application, difficulty in taking into account both deflagration and detonation in the construction of reaction kinetic models. Based on evolutionary algorithm and simplex method, a method for quickly determining the optimal reaction kinetic parameters of a simplified reaction model for reproducing flame and detonation target characteristics is proposed. Compared with the traditional method of solving the optimal reaction kinetic parameters of a simplified reaction model based on genetic algorithm or graphical method, the parameter development speed is greatly improved and the parameter calculation error is reduced. The present invention is suitable for the calculation of most combustion and explosion scenarios (including premixed and non-premixed combustion processes), and can be used for computational fluid dynamics simulation and theoretical analysis of phenomena such as deflagration, detonation, and deflagration to detonation, and has the characteristics of high accuracy, wide scope of application and high development efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 A flowchart of a simplified chemical reaction kinetics model construction method based on an evolutionary algorithm of the present invention;

[0044] Figure 2 It is a flowchart of the centroid-based evolutionary algorithm;

[0045] Figure 3 Schematic diagram of the principle of accelerating convergence of the centroid-based evolutionary algorithm;

[0046] Figure 4 This is the flow chart of the simplex method algorithm;

[0047] Figure 5a , Figure 5b It is the error trend diagram for solving in the optimization process; among them, Figure 5a is the trend of solution error in the iterative optimization process of the centroid-based evolutionary algorithm, Figure 5b The trend of solution error in the iterative optimization process of the simplex method;

[0048] Figure 6 The distribution of flame characteristic parameters calculated using the optimized simplified chemical reaction parameters; the line graph represents the theoretical calculation results, and the scattered points represent the numerical calculation results;

[0049] Figure 7 The distribution of detonation wave characteristic parameters calculated using the optimized simplified chemical reaction parameters. DETAILED DESCRIPTION

[0050] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0051] like Figure 1 As shown, a simplified chemical reaction kinetics model construction method based on an evolutionary algorithm of the present invention comprises the following steps:

[0052] Step 1, according to experimental data or detailed chemical reaction mechanism, the laminar combustion velocity, laminar flame thickness, adiabatic flame temperature, constant volume flame temperature, CJ (Chapman-Jouguet) detonation velocity, half-reaction width and other combustible flame and detonation target characteristic parameters are obtained;

[0053] Step 2: Establish a control equation group for describing the one-dimensional laminar flame and detonation development process. Solving the control equation group can obtain flame and detonation characteristic parameters such as laminar combustion velocity, laminar flame thickness, adiabatic flame temperature, constant volume flame temperature, CJ detonation velocity, and half-reaction width;

[0054] Step 3, estimate the upper and lower limits of the range of simplified chemical reaction kinetic parameters such as activation energy, specific heat ratio, calorific value of combustion, pre-exponential factor, thermal diffusion coefficient, relative molecular mass, and the initial value of iteration;

[0055] Step 4: Substitute the estimated iterative initial value in step 3 into the evolutionary algorithm for solution, and obtain a set of optimized simplified chemical reaction kinetic parameters within the value range; substitute the optimized simplified chemical reaction kinetic parameters into the control equation group and solve the flame and detonation characteristic parameters;

[0056] Step 5: Evaluate the solution error between the flame and detonation characteristic parameters obtained by solving the control equations in step 4 and the target characteristic parameters obtained in step 1, and use the error as the target optimization function of the evolutionary algorithm; if the error is greater than the threshold, continue to use the evolutionary algorithm to iteratively optimize the simplified chemical reaction kinetic parameters and perform error evaluation until the solution error of the control equations meets the predetermined requirements; preferably, the threshold is 10 -3 .

[0057] Step 6: Use the simplex method to locally optimize the simplified chemical reaction kinetic parameters obtained in step 5 until the error of solving the control equation group is less than the set value. At this time, the simplified chemical reaction kinetic parameters obtained by optimization can be used in the computational fluid dynamics analysis to accurately reproduce the target characteristic parameters of the combustible flame and detonation. Preferably, the set value is 10 -5 .

[0058] Specifically, the step 1 includes:

[0059] By conducting experimental measurements or using detailed chemical reaction mechanism calculations, the laminar combustion velocity of combustibles, laminar flame thickness, adiabatic flame temperature, constant volume flame temperature, CJ detonation velocity, half-reaction width and other combustible flame and detonation target characteristic parameters can be obtained. Among them, laminar flame speed refers to the propagation speed of the flame surface relative to the unburned gas; laminar flame thickness refers to the sum of the widths of the preheating zone and the chemical reaction zone. In the present invention, the laminar flame thickness is defined based on the temperature distribution, that is, it is characterized by the ratio of the combustion temperature rise to the maximum temperature gradient; adiabatic flame temperature refers to the temperature that the combustion products can reach when the combustible gas is completely burned under adiabatic conditions; constant volume flame temperature refers to the temperature that the combustion products can reach when the combustible gas is completely burned under constant volume conditions; CJ detonation velocity refers to the simplification of the detonation wave into a one-dimensional discontinuous surface with infinite reaction rate in the Chapman-Jouguet (CJ) theory, combining the continuity equation and the momentum equation to obtain the Rayleigh line, and further considering the energy equation and eliminating the temperature using the gas state equation to obtain the Hugoniot curve. The point where the upper branch of the Rayleigh line is tangent to the Hugoniot curve corresponds to the minimum possible detonation velocity, which is the CJ detonation velocity; the half-reaction width refers to the distance between the position where the fuel mass fraction Y = 0.5 and the shock wave surface in the detonation wave structure.

[0060] Specifically, the step 2 includes:

[0061] The control equations describing the heat conduction and energy release process are established to solve the one-dimensional laminar flame characteristic parameters:

[0062] (1)

[0063] (2)

[0064] (3)

[0065] (4)

[0066] (5)

[0067] in, Indicates the horizontal direction, represents the calculation of the initial density, represents the current density, T0 represents the initial temperature of calculation, T represents the current temperature, represents the specific heat at constant volume, represents the specific heat capacity at constant pressure, is the thermal diffusion coefficient, represents the chemical reaction source term, A represents the pre-exponential factor, represents the activation energy, Y represents the mass fraction of the unburned reactants, q represents the calorific value of combustion, represents the laminar flame speed, is the adiabatic flame temperature, represents the constant volume flame temperature, represents the laminar flame thickness, represents the maximum value of the absolute value of the temperature gradient, exp represents the exponential function, and R represents the universal gas constant.

[0068] Establish the governing equations for describing the detonation wave structure:

[0069] (6)

[0070] (7)

[0071] (8)

[0072] (9)

[0073] Where t represents time, U represents the flow velocity of the combustibles, represents the speed of sound under initial conditions, E represents the specific total energy, c represents the current speed of sound, represents the initial pressure, p represents the current pressure, represents the specific heat ratio, represents the CJ detonation velocity, represents the half-reaction width, and They represent the x-coordinates corresponding to the mass fractions of unburned reactants of 1 and 0.5 respectively. The flame and detonation characteristic parameters can be obtained by solving the above two sets of equations.

[0074] Furthermore, the step 3 comprises:

[0075] Estimate the upper and lower limits of the value range of simplified chemical reaction kinetic parameters such as activation energy, specific heat ratio, heat of combustion, pre-exponential factor, thermal diffusion coefficient, relative molecular mass, and the initial value of the iteration. The value range will limit the optimization search range of the subsequent evolutionary algorithm and affect the convergence speed of the optimization results; when the value range is too large, it may cause the evolutionary algorithm parameter search range to be too wide, thereby increasing the time required for the convergence of the optimization results. Conversely, if the value range is too small, it may be impossible to search for the simplified chemical reaction parameters required to meet the solution error, which will lead to the failure of iterative optimization. In addition, the value range of the simplified chemical reaction parameters can be set differently for each parameter according to the type of combustible material; the initial value of the iteration can be set to the average value of the upper and lower limits of the corresponding value range.

[0076] Specifically, the step 4 includes:

[0077] The present invention adopts a centroid-based evolutionary algorithm, and the mathematical description of the evolutionary algorithm is as follows: Determine the maximum evolutionary step length of the centroid-based evolutionary algorithm , the number of subpopulation individuals K, the data dimension D, determine the population size N=2K D; Initialize N individuals according to the iterative initial value Population , i represents the individual number, the data dimension of each individual is D, and an empty set V is established to store newly generated individuals. When the calculated target optimization function value does not reach the stopping condition, K individuals are selected from the population P to form a sub-population , using subpopulation U s All individuals in calculate the current center of mass c according to formula (11) m In the interval Internal random value determines the evolution step length According to formula (10), from the subpopulation U s Randomly select individuals And using the centroid c m Generate new individuals If the calculated objective optimization function value is > , then the individual Add to set V. Take The first N individuals with the largest value of the objective optimization function update the population P. Represents the union. Repeat the above iterative optimization process until the target optimization function value calculated by the individuals in the population P reaches the predetermined stop criterion, and output the best individual in the population P (the individual when the target optimization function value is the largest) as the target optimization result. The algorithm flow chart is shown in Figure 2 shown.

[0078] (10)

[0079] (11)

[0080] in, represents the new individuals generated in the population, represents an individual in the population P, represents the step length, c m Represents the use of subpopulation U s Calculate the centroid, Represents the subpopulation U s The individuals selected from represents the subpopulation U s Any individual in the population, W represents the total mass of individuals in the population, and f represents an arbitrary function relationship. In the present invention, the population individual These are the simplified chemical reaction kinetic parameters to be optimized. The data dimension D=6, which represent activation energy, specific heat ratio, calorific value of combustion, pre-exponential factor, thermal diffusion coefficient, and relative molecular mass respectively. The function relationship f is the error relationship between the solution of the control equations for laminar flame and detonation development process and the target value.

[0081] This method uses the centroid definition to create the evolution direction of individuals in the population, so that according to the target optimization function value, individuals with large calculation errors in the population are moved to the area with smaller calculation errors in the value interval, thereby achieving the purpose of accelerating the convergence of calculation errors. The schematic diagram of the algorithm's accelerated convergence principle is shown in Figure 3 As shown in the figure, through the subpopulation U s The individual u in r With the centroid c m Determine the direction of population evolution, and then use this evolution direction to transform individuals in population P Move to new instance , so that the individuals in the population are closer to the global minimum point and the purpose of accelerating the convergence of calculation errors is achieved.

[0082] Specifically, the step 5 includes:

[0083] The flame and detonation characteristic parameters ( , , , , , ) is compared with the target characteristic parameters in step 1 and the solution error is quantified. The solution error is defined as:

[0084] (12)

[0085] Among them, error represents the solution error, i represents the flame and detonation characteristic parameter index, Represent the flame and detonation characteristic parameters respectively ( , , , , , ), Represents the corresponding target characteristic parameter. The evolutionary algorithm will minimize the solution error by optimizing and simplifying the chemical reaction kinetic parameters, that is, the solution error of the control equation group is used as the target optimization function of the evolutionary algorithm.

[0086] Specifically, the step 6 includes:

[0087] The simplex method is an optimization scheme for multivariable minimization problems based on heuristic rules. The simplex method was first proposed by John Nelder and Roger Mead in 1965, so it is also called the Nelder-Mead method. This method constructs an iterative optimization strategy for solutions based on the concept of simplex and does not rely on the derivative information of the function. It is suitable for function optimization problems where analytical expressions are difficult or impossible to obtain. For n-dimensional optimization problems, first construct an n+1-dimensional simplex, calculate the function values ​​of the simplex vertices, and then analyze and compare the vertex function values. New vertices and simplexes are constructed through reflection, diffusion, contraction and other operations until the convergence conditions are reached. For n-dimensional minimization problems, this method is used to search for the function to be optimized. The minimum process is as follows Figure 4 As shown:

[0088] (1) Initialize n+1 points , ,……, , as the vertices of the simplex; initialize the reflection coefficient, expansion coefficient, contraction coefficient and retraction coefficient respectively: a=1, b=2, c=0.5, d=0.5;

[0089] (2) Based on The values ​​of are sorted from small to large, assuming: ,in, It is called the optimal point. It is called the worst point. It is called the second difference point, which checks whether the convergence condition is met;

[0090] (3) Abandon the worst point , calculate the average of the first n points , calculate the reflection point ;

[0091] (4) If Better than But worse than , then use replace Construct a new simplex and continue with step (2);

[0092] (5) If Better than , then calculate the extension point ,if Better than , then use replace Construct a new simplex and continue with step (2); otherwise, use replace Construct a new simplex and continue with step (2);

[0093] (6) If Better than But worse than , then calculate the external contraction point ,if Better than , then use replace Construct a new simplex and continue with step (2); otherwise, proceed to step (7);

[0094] (7) If Worse than , then calculate the inner contraction point ,if Better than , then use replace Construct a new simplex and continue with step (2); otherwise, proceed to step (8);

[0095] (8) Use all points except the current optimal point Replace it with , then continue with step (2).

[0096] This method is sensitive to the initial estimate and can only search for a local optimal solution near the initial value rather than a global optimal solution. Therefore, in the present invention, an evolutionary algorithm is first used to perform a global optimization of simplified chemical reaction parameters until the solution error is less than 10 -3 To narrow the search range, the optimization result of the evolutionary algorithm is then used as the initial estimate of the simplex method to perform local optimization until the solution error is less than 10 -5 The steps of using the simplex method to optimize and simplify chemical reaction parameters in the present invention are as follows:

[0097] (1) Use the optimization parameters obtained by the evolutionary algorithm as the initial estimate of the simplex method, and create a simplex around the initial estimate. In this model, there are six reaction parameters (activation energy, specific heat ratio, heat release rate, pre-exponential factor, thermal diffusion coefficient, relative molecular mass), so there are seven edges. The first vertex is defined by the initial estimate, that is, the result of the evolutionary algorithm; each of the other vertices is created by adding 5% to the value of one of the variables while keeping the other variables unchanged;

[0098] (2) Sort each “individual” and calculate the error between each “individual” and the target characteristic according to formula (12);

[0099] (3) Generate a new vertex by reflecting the worst point, and then re-divide the simplex through four basic processes: reflection, expansion, contraction, and retreat, so as to improve itself and approach the optimal state.

[0100] Example:

[0101] The present invention provides a simplified chemical reaction kinetics model construction method based on an evolutionary algorithm, which specifically comprises the following steps:

[0102] Step 1: Obtain the laminar combustion velocity, laminar flame thickness, adiabatic flame temperature, constant volume flame temperature, CJ detonation velocity, half-reaction width and other combustible flame and detonation target characteristic parameters based on experimental data or detailed chemical reaction mechanism:

[0103] In this embodiment, simplified chemical reaction kinetic parameters suitable for describing the combustion process of a hydrogen-air mixture with an equivalence ratio of 1 at an initial temperature T0 = 298 K and an initial pressure P0 = 101325 Pa are developed. The flame and detonation characteristic parameters formed under this condition can be obtained by calculation using a detailed chemical reaction mechanism, and the specific parameter values ​​are shown in Table 1.

[0104] Table 1 Flame and detonation target characteristic parameters

[0105]

[0106] Step 2: Establish a control equation group for describing the one-dimensional laminar flame and detonation development process. Solving the control equation group can obtain flame and detonation characteristic parameters such as laminar combustion velocity, laminar flame thickness, adiabatic flame temperature, constant volume flame temperature, CJ detonation velocity, and half-reaction width;

[0107] Step 3: estimate the upper and lower limits of the value range and the initial value of iteration of simplified chemical reaction kinetic parameters such as activation energy, specific heat ratio, calorific value of combustion, pre-exponential factor, thermal diffusion coefficient, relative molecular mass, etc. In this embodiment, the value range and initial value of iteration corresponding to each simplified chemical reaction parameter are shown in Table 2:

[0108] Table 2 Simplified chemical reaction parameters corresponding to the value range and iterative initial value

[0109]

[0110] Step 4: Substitute the estimated iterative initial value in step 3 into the evolutionary algorithm to solve and obtain a set of optimized simplified chemical reaction kinetic parameters within the value range; substitute the optimized simplified chemical reaction kinetic parameters into the control equation group and solve the flame and detonation characteristic parameters;

[0111] Step 5: Evaluate the solution error between the flame and detonation characteristic parameters obtained by solving the control equations in step 4 and the target characteristic parameters obtained in step 1, and use the error as the target optimization function of the evolutionary algorithm; if the error is greater than 10 -3 Then the simplified chemical reaction kinetic parameters are iteratively optimized and the error is evaluated by using the evolutionary algorithm until the error of the solution of the control equation group meets the predetermined requirements;

[0112] In this embodiment, the maximum evolution step length of the centroid-based evolutionary algorithm is set to , the number of subpopulation individuals K = 7, the data dimension D = 6, and the population size N = 2K × D = 84; after 202 rounds of iterative optimization, the error of the flame and detonation characteristic parameters is 9.83675 × 10 -4 The stopping criterion is reached, and the error decreases with the number of iterations during the optimization process. Figure 5a The simplified chemical reaction parameter values ​​calculated at this time are shown in Table 3, where R represents the universal gas constant, R=8.314 J / (mol·K). The CPU time consumed by the iterative optimization using this method is 134.2 s, while the CPU time consumed by the traditional genetic algorithm optimization to achieve the same solution error is 18040 s, indicating the high efficiency of the current algorithm in developing reaction parameters.

[0113] Table 3 Simplified chemical reaction parameter values ​​obtained by evolutionary algorithm optimization

[0114]

[0115] Step 6: Use the simplex method to locally optimize the simplified chemical reaction kinetic parameters obtained in step 5 until the error of solving the control equations is less than 10 -5 . At this point, the optimized simplified chemical reaction kinetics parameters can be used in computational fluid dynamics analysis to accurately reproduce the target characteristic parameters of combustible flame and detonation. In this embodiment, the optimized parameters in step 5 are used as the initial values ​​of the simplex method iteration, and the reflection coefficient, expansion coefficient, contraction coefficient and retraction coefficient in the simplex method are initialized as follows: a=1, b=2, c=0.5, d=0.5. After 346 rounds of iterations, the calculated characteristic parameter solution error is 9.7508×10 -6 , which meets the requirements for stopping iterative optimization. The error decreases with the number of iterations during the optimization process. Figure 5b The simplified chemical reaction parameter values ​​calculated at this time are shown in Table 4, and the comparison between the flame and detonation characteristic parameters calculated using the optimized simplified chemical reaction parameter values ​​and the target characteristic parameters is shown in Table 5:

[0116] Table 4 Simplified chemical reaction parameter values ​​obtained by simplex method optimization

[0117]

[0118] Table 5 Comparison of flame and detonation characteristic parameters calculated by optimizing chemical reaction parameter values ​​with target characteristic parameters

[0119]

[0120] The simplified chemical reaction kinetic parameters obtained by the current algorithm optimization are substituted into the computational fluid dynamics control equations and numerically solved. The distribution of one-dimensional laminar flame characteristic parameters obtained by numerical calculation is compared with the theoretical values ​​to verify the accuracy of the current simplified chemical reaction kinetic parameters. The comparison results are shown in Figure 6 As shown in the figure, it can be seen that the numerical simulation results are in good agreement with the theoretical solution results, and the spatial distribution of each flame characteristic parameter is accurately predicted. The distribution of components, velocity, reaction rate, and pressure near the detonation wave obtained by using the optimized simplified chemical reaction kinetic parameters is shown in the figure. Figure 7 The results show that the CJ detonation velocity and half-reaction width calculated using the optimized parameters It is in good agreement with the theoretical value.

[0121] Although the above describes the illustrative specific embodiments of the present invention to facilitate the understanding of the present invention by those skilled in the art, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

Claims

1. A method for constructing a simplified chemical reaction kinetics model based on an evolutionary algorithm, characterized in that: The steps include: Step 1, obtaining the combustible flame and detonation target characteristic parameters according to experimental data or by calculation of a detailed chemical reaction mechanism, wherein the combustible flame and detonation target characteristic parameters include laminar combustion velocity, laminar flame thickness, adiabatic flame temperature, constant volume flame temperature, CJ detonation velocity, and half reaction width; Step 2, establishing a control equation group for describing the one-dimensional laminar flame and detonation development process, solving the control equation group to obtain flame and detonation characteristic parameters, wherein the flame and detonation characteristic parameters include laminar combustion velocity, laminar flame thickness, adiabatic flame temperature, constant volume flame temperature, CJ detonation velocity, and half reaction width; Step 3, estimating the upper and lower limits of the value range of simplified chemical reaction kinetic parameters and the initial value of iteration, wherein the simplified chemical reaction kinetic parameters include activation energy, specific heat ratio, calorific value of combustion, pre-exponential factor, thermal diffusion coefficient, and relative molecular mass; Step 4: Substitute the estimated iterative initial value in step 3 into the evolutionary algorithm to solve and obtain a set of optimized simplified chemical reaction kinetic parameters within the value range; substitute the optimized simplified chemical reaction kinetic parameters into the control equation group constructed in step 2 and solve the flame and detonation characteristic parameters; Step 5, evaluating the solution error between the flame and detonation characteristic parameters obtained by solving the control equations in step 4 and the target characteristic parameters obtained in step 1, and using the solution error as the target optimization function of the evolutionary algorithm; If the error is greater than the threshold, the simplified chemical reaction kinetic parameters are iteratively optimized using the evolutionary algorithm and the error is evaluated until the error of the solution of the control equation group meets the predetermined requirements; Step 6: Use the simplex method to locally optimize the simplified chemical reaction kinetic parameters obtained in step 5 until the error of solving the control equation group is less than the set value; use the optimized simplified chemical reaction kinetic parameters in the computational fluid dynamics analysis to calculate and accurately reproduce the target characteristic parameters of the combustible flame and detonation.

2. A method for constructing a simplified chemical reaction kinetics model based on an evolutionary algorithm according to claim 1, characterized in that: The step 1 comprises: obtaining the characteristic parameters of the combustible flame and detonation target by conducting experimental measurements or solving the detailed chemical reaction mechanism according to the type of combustible; wherein, the laminar flame speed refers to the propagation speed of the flame surface relative to the unburned gas; the laminar flame thickness refers to the sum of the widths of the preheating zone and the chemical reaction zone; the adiabatic flame temperature refers to the temperature that the combustion products can reach when the combustible gas is completely burned under adiabatic conditions; the constant volume flame temperature refers to the temperature that the combustion products can reach when the combustible gas is completely burned under constant volume conditions; the CJ detonation velocity refers to the minimum detonation wave velocity calculated by simplifying the detonation wave into a one-dimensional discontinuous surface with infinite reaction rate in the Chapman-Jouguet theory; the half-reaction width refers to the distance between the position where the fuel mass fraction Y = 0.5 and the position where the shock wave surface is located in the detonation wave structure.

3. A method for constructing a simplified chemical reaction kinetics model based on an evolutionary algorithm according to claim 1, characterized in that: The step 2 comprises: The control equations describing the heat conduction and energy release process are established to solve the one-dimensional laminar flame characteristic parameters: （1） （2） （3） （4） （5） in, Indicates the horizontal direction, represents the calculation of the initial density, represents the current density, T0 represents the initial temperature of calculation, T represents the current temperature, represents the specific heat at constant volume, represents the specific heat capacity at constant pressure, is the thermal diffusion coefficient, represents the chemical reaction source term, A represents the pre-exponential factor, represents the activation energy, Y represents the mass fraction of the unburned reactants, q represents the calorific value of combustion, represents the laminar flame speed, is the adiabatic flame temperature, represents the constant volume flame temperature, represents the laminar flame thickness, represents the maximum value of the absolute value of the temperature gradient, exp represents the exponential function, and R represents the universal gas constant; Establish the governing equations for describing the detonation wave structure: （6） （7） （8） （9） Where t represents time, U represents the flow velocity of the combustibles, represents the speed of sound under initial conditions, E represents the specific total energy, c represents the current speed of sound, represents the initial pressure, p represents the current pressure, represents the specific heat ratio, represents the CJ detonation velocity, represents the half-reaction width, and They represent the x-coordinates corresponding to the mass fractions of unburned reactants of 1 and 0.5 respectively. The flame and detonation characteristic parameters are obtained by solving the two sets of equations.

4. The method for constructing a simplified chemical reaction kinetics model based on an evolutionary algorithm according to claim 1, characterized in that: The step 3 comprises: Each parameter uses a different value range, and the initial value of the iteration is the average of the upper and lower limits of the corresponding value range.

5. The method for constructing a simplified chemical reaction kinetics model based on an evolutionary algorithm according to claim 1, characterized in that: In step 4, a centroid-based evolutionary algorithm is adopted, and the centroid definition is used to create the evolution direction of individuals in the population. According to the target optimization function value, individuals with larger calculation errors in the population are moved to the area with smaller calculation errors in the value interval, thereby accelerating the convergence of calculation errors.

6. A method for constructing a simplified chemical reaction kinetics model based on an evolutionary algorithm according to claim 5, characterized in that: The evolutionary algorithm includes: determining the maximum evolutionary step length of the centroid-based evolutionary algorithm , the number of subpopulation individuals K, the data dimension D, determine the population size N = 2K × D; initialize the population containing N individuals according to the iterative initial value Population , , the data dimension of each individual is D, and an empty set V is established to store the newly generated individuals; when the calculated target optimization function value does not reach the stopping condition, K individuals are selected from the population P to form a sub-population , using subpopulation U s All individuals in calculate the current center of mass c according to formula (11) m ; In the interval Internal random value determines the evolution step length According to formula (10), from subpopulation U s Randomly select individuals And using the centroid c m Generate new individuals ; If the calculated objective optimization function value > , then the individual Join set V; take The first N individuals with the largest target optimization function value in the population P are used to update the population P; the above iterative optimization process is repeated until the target optimization function value calculated by the individuals in the population P reaches the predetermined stop criterion, and the best individual in the population P is output as the target optimization result; the best individual is the individual when the target optimization function value is the largest; （10） （11） in, represents the new individuals generated in the population, represents an individual in the population P, represents the step length, c m Represents the use of subpopulation U s Calculate the centroid, Represents the subpopulation U s The individuals selected from represents the subpopulation U s Any individual in the population, W represents the total mass of individuals in the population, and f represents an arbitrary function relationship; These are the simplified chemical reaction kinetic parameters to be optimized. The data dimension D=6, which represent activation energy, specific heat ratio, calorific value of combustion, pre-exponential factor, thermal diffusion coefficient, and relative molecular mass respectively. The function relationship f is the error relationship between the solution of the control equations for laminar flame and detonation development process and the target value.

7. The method for constructing a simplified chemical reaction kinetics model based on an evolutionary algorithm according to claim 1, characterized in that: The solution errors in step 5 include: The flame and detonation characteristic parameters ( , , , , , ) is compared with the target characteristic parameters in step 1 and the solution error is quantified. The solution error is defined as: ； Among them, error represents the solution error, i represents the flame and detonation characteristic parameter index, Represent the flame and detonation characteristic parameters respectively ( , , , , , ), Represents the corresponding target characteristic parameters. The evolutionary algorithm will minimize the solution error by optimizing and simplifying the chemical reaction kinetic parameters, that is, the solution error of the control equation group is used as the target optimization function of the evolutionary algorithm.

8. The method for developing a simplified chemical reaction kinetics model based on an evolutionary algorithm according to claim 1, characterized in that: The simplex method used in step 6 includes: For n-dimensional optimization problems, we first construct an n+1-dimensional simplex, calculate the function values ​​of the simplex vertices, and then analyze and compare the vertex function values. We construct new vertices and simplexes through reflection, diffusion, contraction and other operations until the convergence conditions are met.

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